Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.5% → 97.7%

Time: 7.1s

Alternatives: 7

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((y - x) * z) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Python

def code(x, y, z, t):
	return x + (((y - x) * z) / t)

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(y - x) * z) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((y - x) * z) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((y - x) * z) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}

Python

def code(x, y, z, t):
	return x + (((y - x) * z) / t)

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(y - x) * z) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((y - x) * z) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \frac{z}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}

Python

def code(x, y, z, t):
	return x + ((y - x) * (z / t))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - x) * Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - x) * (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.9%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Step-by-step derivation

   1. associate-/l* 98.0%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

3. Simplified 98.0%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}} \]
4. Add Preprocessing

5. Final simplification 98.0%

   \[\leadsto x + \left(y - x\right) \cdot \frac{z}{t} \]
6. Add Preprocessing

Alternative 2: 49.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -0.056 \lor \neg \left(t \leq -5 \cdot 10^{-96}\right) \land t \leq 4 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.5e+38)
   x
   (if (or (<= t -0.056) (and (not (<= t -5e-96)) (<= t 4e-49)))
     (* z (/ x (- t)))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+38) {
		tmp = x;
	} else if ((t <= -0.056) || (!(t <= -5e-96) && (t <= 4e-49))) {
		tmp = z * (x / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.5d+38)) then
        tmp = x
    else if ((t <= (-0.056d0)) .or. (.not. (t <= (-5d-96))) .and. (t <= 4d-49)) then
        tmp = z * (x / -t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+38) {
		tmp = x;
	} else if ((t <= -0.056) || (!(t <= -5e-96) && (t <= 4e-49))) {
		tmp = z * (x / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.5e+38:
		tmp = x
	elif (t <= -0.056) or (not (t <= -5e-96) and (t <= 4e-49)):
		tmp = z * (x / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.5e+38)
		tmp = x;
	elseif ((t <= -0.056) || (!(t <= -5e-96) && (t <= 4e-49)))
		tmp = Float64(z * Float64(x / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.5e+38)
		tmp = x;
	elseif ((t <= -0.056) || (~((t <= -5e-96)) && (t <= 4e-49)))
		tmp = z * (x / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.5e+38], x, If[Or[LessEqual[t, -0.056], And[N[Not[LessEqual[t, -5e-96]], $MachinePrecision], LessEqual[t, 4e-49]]], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999998e38 or -0.0560000000000000012 < t < -4.99999999999999995e-96 or 3.99999999999999975e-49 < t

   1. Initial program 88.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 88.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 90.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   7. Simplified 90.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   8. Taylor expanded in x around inf 61.0%

      \[\leadsto \color{blue}{x} \]

   if -4.4999999999999998e38 < t < -0.0560000000000000012 or -4.99999999999999995e-96 < t < 3.99999999999999975e-49

   1. Initial program 98.2%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 57.1%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.1%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{t} \]

      2. distribute-lft-neg-out 57.1%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{t} \]

      3. *-commutative 57.1%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]

   5. Simplified 57.1%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]
   6. Step-by-step derivation

      1. div-inv 57.1%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(-x\right)\right) \cdot \frac{1}{t}} \]

      2. *-commutative 57.1%

         \[\leadsto x + \color{blue}{\left(\left(-x\right) \cdot z\right)} \cdot \frac{1}{t} \]

      3. *-commutative 57.1%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(-x\right)\right)} \cdot \frac{1}{t} \]

      4. add-sqr-sqrt 28.4%

         \[\leadsto x + \left(z \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) \cdot \frac{1}{t} \]

      5. sqrt-unprod 31.6%

         \[\leadsto x + \left(z \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) \cdot \frac{1}{t} \]

      6. sqr-neg 31.6%

         \[\leadsto x + \left(z \cdot \sqrt{\color{blue}{x \cdot x}}\right) \cdot \frac{1}{t} \]

      7. sqrt-unprod 4.8%

         \[\leadsto x + \left(z \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \cdot \frac{1}{t} \]

      8. add-sqr-sqrt 9.2%

         \[\leadsto x + \left(z \cdot \color{blue}{x}\right) \cdot \frac{1}{t} \]

      9. remove-double-neg 9.2%

         \[\leadsto x + \color{blue}{\left(-\left(-z \cdot x\right)\right)} \cdot \frac{1}{t} \]

      10. distribute-rgt-neg-out 9.2%

          \[\leadsto x + \left(-\color{blue}{z \cdot \left(-x\right)}\right) \cdot \frac{1}{t} \]

      11. cancel-sign-sub-inv 9.2%

          \[\leadsto \color{blue}{x - \left(z \cdot \left(-x\right)\right) \cdot \frac{1}{t}} \]

      12. div-inv 9.2%

          \[\leadsto x - \color{blue}{\frac{z \cdot \left(-x\right)}{t}} \]

      13. associate-/l* 7.5%

          \[\leadsto x - \color{blue}{z \cdot \frac{-x}{t}} \]

      14. add-sqr-sqrt 2.6%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t} \]

      15. sqrt-unprod 26.8%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t} \]

      16. sqr-neg 26.8%

          \[\leadsto x - z \cdot \frac{\sqrt{\color{blue}{x \cdot x}}}{t} \]

      17. sqrt-unprod 26.2%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t} \]

      18. add-sqr-sqrt 51.9%

          \[\leadsto x - z \cdot \frac{\color{blue}{x}}{t} \]

   7. Applied egg-rr 51.9%

      \[\leadsto \color{blue}{x - z \cdot \frac{x}{t}} \]

   8. Taylor expanded in z around inf 50.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 50.9%

         \[\leadsto \color{blue}{-\frac{x \cdot z}{t}} \]

      2. *-commutative 50.9%

         \[\leadsto -\frac{\color{blue}{z \cdot x}}{t} \]

      3. distribute-frac-neg2 50.9%

         \[\leadsto \color{blue}{\frac{z \cdot x}{-t}} \]

      4. associate-*r/ 47.5%

         \[\leadsto \color{blue}{z \cdot \frac{x}{-t}} \]

   10. Simplified 47.5%

       \[\leadsto \color{blue}{z \cdot \frac{x}{-t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -0.056 \lor \neg \left(t \leq -5 \cdot 10^{-96}\right) \land t \leq 4 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{z}{\frac{-t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.2e+38)
   x
   (if (<= t -5.6e-5)
     (* z (/ x (- t)))
     (if (<= t -3e-96) x (if (<= t 3.4e-53) (/ z (/ (- t) x)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e+38) {
		tmp = x;
	} else if (t <= -5.6e-5) {
		tmp = z * (x / -t);
	} else if (t <= -3e-96) {
		tmp = x;
	} else if (t <= 3.4e-53) {
		tmp = z / (-t / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.2d+38)) then
        tmp = x
    else if (t <= (-5.6d-5)) then
        tmp = z * (x / -t)
    else if (t <= (-3d-96)) then
        tmp = x
    else if (t <= 3.4d-53) then
        tmp = z / (-t / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e+38) {
		tmp = x;
	} else if (t <= -5.6e-5) {
		tmp = z * (x / -t);
	} else if (t <= -3e-96) {
		tmp = x;
	} else if (t <= 3.4e-53) {
		tmp = z / (-t / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.2e+38:
		tmp = x
	elif t <= -5.6e-5:
		tmp = z * (x / -t)
	elif t <= -3e-96:
		tmp = x
	elif t <= 3.4e-53:
		tmp = z / (-t / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.2e+38)
		tmp = x;
	elseif (t <= -5.6e-5)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (t <= -3e-96)
		tmp = x;
	elseif (t <= 3.4e-53)
		tmp = Float64(z / Float64(Float64(-t) / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.2e+38)
		tmp = x;
	elseif (t <= -5.6e-5)
		tmp = z * (x / -t);
	elseif (t <= -3e-96)
		tmp = x;
	elseif (t <= 3.4e-53)
		tmp = z / (-t / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.2e+38], x, If[LessEqual[t, -5.6e-5], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-96], x, If[LessEqual[t, 3.4e-53], N[(z / N[((-t) / x), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.19999999999999985e38 or -5.59999999999999992e-5 < t < -3e-96 or 3.4e-53 < t

   1. Initial program 88.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 88.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 90.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   7. Simplified 90.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   8. Taylor expanded in x around inf 61.0%

      \[\leadsto \color{blue}{x} \]

   if -3.19999999999999985e38 < t < -5.59999999999999992e-5

   1. Initial program 93.4%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 54.7%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 54.7%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{t} \]

      2. distribute-lft-neg-out 54.7%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{t} \]

      3. *-commutative 54.7%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]

   5. Simplified 54.7%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]
   6. Step-by-step derivation

      1. div-inv 54.7%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(-x\right)\right) \cdot \frac{1}{t}} \]

      2. *-commutative 54.7%

         \[\leadsto x + \color{blue}{\left(\left(-x\right) \cdot z\right)} \cdot \frac{1}{t} \]

      3. *-commutative 54.7%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(-x\right)\right)} \cdot \frac{1}{t} \]

      4. add-sqr-sqrt 18.7%

         \[\leadsto x + \left(z \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) \cdot \frac{1}{t} \]

      5. sqrt-unprod 19.7%

         \[\leadsto x + \left(z \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) \cdot \frac{1}{t} \]

      6. sqr-neg 19.7%

         \[\leadsto x + \left(z \cdot \sqrt{\color{blue}{x \cdot x}}\right) \cdot \frac{1}{t} \]

      7. sqrt-unprod 7.5%

         \[\leadsto x + \left(z \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \cdot \frac{1}{t} \]

      8. add-sqr-sqrt 8.1%

         \[\leadsto x + \left(z \cdot \color{blue}{x}\right) \cdot \frac{1}{t} \]

      9. remove-double-neg 8.1%

         \[\leadsto x + \color{blue}{\left(-\left(-z \cdot x\right)\right)} \cdot \frac{1}{t} \]

      10. distribute-rgt-neg-out 8.1%

          \[\leadsto x + \left(-\color{blue}{z \cdot \left(-x\right)}\right) \cdot \frac{1}{t} \]

      11. cancel-sign-sub-inv 8.1%

          \[\leadsto \color{blue}{x - \left(z \cdot \left(-x\right)\right) \cdot \frac{1}{t}} \]

      12. div-inv 8.1%

          \[\leadsto x - \color{blue}{\frac{z \cdot \left(-x\right)}{t}} \]

      13. associate-/l* 8.1%

          \[\leadsto x - \color{blue}{z \cdot \frac{-x}{t}} \]

      14. add-sqr-sqrt 0.6%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t} \]

      15. sqrt-unprod 22.9%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t} \]

      16. sqr-neg 22.9%

          \[\leadsto x - z \cdot \frac{\sqrt{\color{blue}{x \cdot x}}}{t} \]

      17. sqrt-unprod 36.1%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t} \]

      18. add-sqr-sqrt 54.8%

          \[\leadsto x - z \cdot \frac{\color{blue}{x}}{t} \]

   7. Applied egg-rr 54.8%

      \[\leadsto \color{blue}{x - z \cdot \frac{x}{t}} \]

   8. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 47.3%

         \[\leadsto \color{blue}{-\frac{x \cdot z}{t}} \]

      2. *-commutative 47.3%

         \[\leadsto -\frac{\color{blue}{z \cdot x}}{t} \]

      3. distribute-frac-neg2 47.3%

         \[\leadsto \color{blue}{\frac{z \cdot x}{-t}} \]

      4. associate-*r/ 47.4%

         \[\leadsto \color{blue}{z \cdot \frac{x}{-t}} \]

   10. Simplified 47.4%

       \[\leadsto \color{blue}{z \cdot \frac{x}{-t}} \]

   if -3e-96 < t < 3.4e-53

   1. Initial program 98.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 57.4%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.4%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{t} \]

      2. distribute-lft-neg-out 57.4%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{t} \]

      3. *-commutative 57.4%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]

   5. Simplified 57.4%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]
   6. Step-by-step derivation

      1. div-inv 57.4%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(-x\right)\right) \cdot \frac{1}{t}} \]

      2. *-commutative 57.4%

         \[\leadsto x + \color{blue}{\left(\left(-x\right) \cdot z\right)} \cdot \frac{1}{t} \]

      3. *-commutative 57.4%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(-x\right)\right)} \cdot \frac{1}{t} \]

      4. add-sqr-sqrt 29.8%

         \[\leadsto x + \left(z \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) \cdot \frac{1}{t} \]

      5. sqrt-unprod 33.3%

         \[\leadsto x + \left(z \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) \cdot \frac{1}{t} \]

      6. sqr-neg 33.3%

         \[\leadsto x + \left(z \cdot \sqrt{\color{blue}{x \cdot x}}\right) \cdot \frac{1}{t} \]

      7. sqrt-unprod 4.4%

         \[\leadsto x + \left(z \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \cdot \frac{1}{t} \]

      8. add-sqr-sqrt 9.4%

         \[\leadsto x + \left(z \cdot \color{blue}{x}\right) \cdot \frac{1}{t} \]

      9. remove-double-neg 9.4%

         \[\leadsto x + \color{blue}{\left(-\left(-z \cdot x\right)\right)} \cdot \frac{1}{t} \]

      10. distribute-rgt-neg-out 9.4%

          \[\leadsto x + \left(-\color{blue}{z \cdot \left(-x\right)}\right) \cdot \frac{1}{t} \]

      11. cancel-sign-sub-inv 9.4%

          \[\leadsto \color{blue}{x - \left(z \cdot \left(-x\right)\right) \cdot \frac{1}{t}} \]

      12. div-inv 9.4%

          \[\leadsto x - \color{blue}{\frac{z \cdot \left(-x\right)}{t}} \]

      13. associate-/l* 7.4%

          \[\leadsto x - \color{blue}{z \cdot \frac{-x}{t}} \]

      14. add-sqr-sqrt 2.9%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t} \]

      15. sqrt-unprod 27.4%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t} \]

      16. sqr-neg 27.4%

          \[\leadsto x - z \cdot \frac{\sqrt{\color{blue}{x \cdot x}}}{t} \]

      17. sqrt-unprod 24.7%

          \[\leadsto x - z \cdot \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t} \]

      18. add-sqr-sqrt 51.5%

          \[\leadsto x - z \cdot \frac{\color{blue}{x}}{t} \]

   7. Applied egg-rr 51.5%

      \[\leadsto \color{blue}{x - z \cdot \frac{x}{t}} \]

   8. Taylor expanded in z around inf 51.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.4%

         \[\leadsto \color{blue}{-\frac{x \cdot z}{t}} \]

      2. *-commutative 51.4%

         \[\leadsto -\frac{\color{blue}{z \cdot x}}{t} \]

      3. associate-*l/ 53.4%

         \[\leadsto -\color{blue}{\frac{z}{t} \cdot x} \]

      4. associate-/r/ 48.1%

         \[\leadsto -\color{blue}{\frac{z}{\frac{t}{x}}} \]

      5. distribute-neg-frac2 48.1%

         \[\leadsto \color{blue}{\frac{z}{-\frac{t}{x}}} \]

   10. Simplified 48.1%

       \[\leadsto \color{blue}{\frac{z}{-\frac{t}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{z}{\frac{-t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+63} \lor \neg \left(x \leq 2.95 \cdot 10^{+87}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.7e+63) (not (<= x 2.95e+87)))
   (* x (- 1.0 (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e+63) || !(x <= 2.95e+87)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.7d+63)) .or. (.not. (x <= 2.95d+87))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e+63) || !(x <= 2.95e+87)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.7e+63) or not (x <= 2.95e+87):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.7e+63) || !(x <= 2.95e+87))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.7e+63) || ~((x <= 2.95e+87)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.7e+63], N[Not[LessEqual[x, 2.95e+87]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.69999999999999968e63 or 2.9499999999999998e87 < x

   1. Initial program 87.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.4%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{t} \]
   4. Step-by-step derivation

      1. mul-1-neg 82.4%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{t} \]

      2. distribute-lft-neg-out 82.4%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{t} \]

      3. *-commutative 82.4%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]

   5. Simplified 82.4%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]

   6. Taylor expanded in x around 0 94.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 94.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]

      2. unsub-neg 94.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]

   8. Simplified 94.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]

   if -3.69999999999999968e63 < x < 2.9499999999999998e87

   1. Initial program 96.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.8%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 85.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 86.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   7. Simplified 86.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+63} \lor \neg \left(x \leq 2.95 \cdot 10^{+87}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+67} \lor \neg \left(x \leq 5.2 \cdot 10^{+87}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.8e+67) (not (<= x 5.2e+87)))
   (- x (* x (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.8e+67) || !(x <= 5.2e+87)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.8d+67)) .or. (.not. (x <= 5.2d+87))) then
        tmp = x - (x * (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.8e+67) || !(x <= 5.2e+87)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.8e+67) or not (x <= 5.2e+87):
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.8e+67) || !(x <= 5.2e+87))
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.8e+67) || ~((x <= 5.2e+87)))
		tmp = x - (x * (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.8e+67], N[Not[LessEqual[x, 5.2e+87]], $MachinePrecision]], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e67 or 5.19999999999999997e87 < x

   1. Initial program 87.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.4%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   6. Step-by-step derivation

      1. *-commutative 82.4%

         \[\leadsto x + -1 \cdot \frac{\color{blue}{z \cdot x}}{t} \]

      2. associate-*l/ 94.3%

         \[\leadsto x + -1 \cdot \color{blue}{\left(\frac{z}{t} \cdot x\right)} \]

      3. neg-mul-1 94.3%

         \[\leadsto x + \color{blue}{\left(-\frac{z}{t} \cdot x\right)} \]

      4. distribute-rgt-neg-out 94.3%

         \[\leadsto x + \color{blue}{\frac{z}{t} \cdot \left(-x\right)} \]

   7. Simplified 94.3%

      \[\leadsto x + \color{blue}{\frac{z}{t} \cdot \left(-x\right)} \]

   if -1.7999999999999999e67 < x < 5.19999999999999997e87

   1. Initial program 96.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.8%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 85.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 86.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

   7. Simplified 86.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+67} \lor \neg \left(x \leq 5.2 \cdot 10^{+87}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (1.0d0 - (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (z / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.9%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 60.4%

   \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{t} \]
4. Step-by-step derivation

   1. mul-1-neg 60.4%

      \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{t} \]

   2. distribute-lft-neg-out 60.4%

      \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{t} \]

   3. *-commutative 60.4%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]

5. Simplified 60.4%

   \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{t} \]

6. Taylor expanded in x around 0 65.2%

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{t}\right)} \]
7. Step-by-step derivation

   1. mul-1-neg 65.2%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{t}\right)}\right) \]

   2. unsub-neg 65.2%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{t}\right)} \]

8. Simplified 65.2%

   \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]

9. Final simplification 65.2%

   \[\leadsto x \cdot \left(1 - \frac{z}{t}\right) \]
10. Add Preprocessing

Alternative 7: 39.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 92.9%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Step-by-step derivation

   1. associate-/l* 98.0%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

3. Simplified 98.0%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \frac{z}{t}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 77.1%

   \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
6. Step-by-step derivation

   1. associate-*r/ 78.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

7. Simplified 78.5%

   \[\leadsto x + \color{blue}{y \cdot \frac{z}{t}} \]

8. Taylor expanded in x around inf 38.5%

   \[\leadsto \color{blue}{x} \]

9. Final simplification 38.5%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))